How to merge vertex groups?
You can do this using the 'Vertex Weight Mix' modifier.

Here, I have an object with two vertex groups I would like to mix, one is a patch on the left and the other contains a patch on the right of the object:



'Vertex Group A' is set to the left patch (the vertex group I want to effect) and 'Vertex Group B' is the right patch (the vertex group I want to add into the other one). I then set the 'Mix Mode' to add and the vertex groups are mixed:



Applying the modifier will cause these mixed weights to be permanently written to the 'Left' vertex group. 

If you want to preserve the contents of the 'Left' vertex group then you can make a copy of it before applying the modifier: